\(\int F d t=m \Delta v\)
\(\int F d t\) is area under \(F-t\) curve
\(m \Delta v \left.=\pi\left(\frac{F_0}{2}\right) \cdot\left(\frac{T_0}{2}\right) \text { [area }=\frac{\pi a b}{2}\right]\)
\(v-v_0 =\frac{\pi F_0 T_0}{4 m}\)
\(v=v_0+\frac{\pi F_0 T_0}{4 m}\)